Tip: Working Problems in Reverse

Here's a quick tip I've gleaned from all my review sessions and such: sometimes it's faster to solve a problem by working it backwards.

The FE is a multiple choice test. You're given four possibilities for each question. You're not supposed to do this, but it is entirely possible that you will encounter a question where it's easier to work each of the four possible answers backwards until you encounter one that gives you the correct result.

Suppose you encounter a function and the answer can be quickly calculated using some obscure algebraic method which you forgot. Your options are A) take a shot in the dark (which will have a success rate of ~25%), B) thumb through the book looking for the method, which you may or may not find in a reasonable amount of time, or C) start plugging in answers 1-4 until you find one that works.

In certain circumstances, C may be the best route.

This isn't always the case. In some cases the "backwards" method is not always apparent or any quicker than the correct way of arriving at the answer. Sometimes the method might really be stated bluntly and found easily in your Reference Manual. But if you encounter something that just straight-up stumps you, you're wasting a lot of time trying to learn it on the fly, and you get to a point where you can just plug and chug more quickly, why not?

If you go through a lot of practice and review materials published, you'll see some obvious cases of this. Others are not so clear, but if you know what to look for, you could find opportunities.

One example of this is integrals and derivatives. They undo each other! So if you're asked to integrate something and you don't remember how, you can always take the derivative of the four possible answers and see which one matches.

This is not the ideal way of doing anything, and it won't work every time. But the two or three problems it works on might be the difference between passing and failing!